Random Matrices: Universality of Local Eigenvalue Statistics up to the Edge
نویسندگان
چکیده
This is a continuation of our earlier paper [25] on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in [25] from the bulk of the spectrum up to the edge. In particular, we prove a variant of the universality results of Soshnikov [23] for the largest eigenvalues, assuming moment conditions rather than symmetry conditions. The main new technical observation is that there is a significant bias in the Cauchy interlacing law near the edge of the spectrum which allows one to continue ensuring the delocalization of eigenvectors.
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